Small-angle neutron scattering study of mesoscale magnetic disordering and skyrmion phase suppression in the frustrated chiral magnet Co6.75Zn6.75Mn6.5

In the frustrated chiral magnet Co6.75Zn6.75Mn6.5, small-angle neutron scattering reveals that the mesoscale chiral magnetism displays strong disorder and the skyrmion phase is nearly entirely suppressed.


Introduction
Small-angle neutron scattering (SANS) is an established technique for scrutinizing mesoscale incommensurately modulated magnetic structures in solids (Mü hlbauer et al., 2019). Nowhere is this clearer than in the study of spiral, vortex, meron and skyrmion phases in various noncentrosymmetric magnets, ranging from the itinerant B20s MnSi (Mü hlbauer et al., 2009) and FeGe (Moskvin et al., 2013), to the intermetallics Co-Zn-Mn (Tokunaga et al., 2015), CeAlGe (Puphal et al., 2020) and Y 3 Co 8 Sn 4 (Takagi et al., 2018), to the insulators Cu 2 OSeO 3 (Seki et al., 2012), GaV 4 Se 8 (Bordá cs et al., 2017) and VOSe 2 O 5 (Kurumaji et al., 2017), to name a few. In itinerant chiral cubic magnets, the antisymmetric Dzyaloshinskii-Moriya interaction (DMI) D arises from the spin-orbit interaction in the presence of broken space inversion, and competes microscopically with a dominant ferromagnetic exchange J. This competition leads to the formation of a long-period helical spiral ground state that modulates with a real-space period / J/D along directions determined by magnetic anisotropy. Typical length scales for the helical modulation range from a few to a few hundred nanometres (Kanazawa et al., 2017;Tokura & Kanazawa, 2021), lying within the range accessible by SANS. Such a length scale is also inherited by topological skyrmions that form out of helical order under a small magnetic field H and near the critical temperature T c . Since fluctuations are crucial for skyrmion phase stability (Mü hlbauer et al., 2009;Kruchkov et al., 2018), the equilibrium skyrmion phase is correspondingly narrow in temperature span, being just a few percent of T c wide directly below T c . Otherwise, the non-topological helical or field-induced helical cone ('conical') phases dominate the rest of the phase diagram (Kanazawa et al., 2017;Tokura & Kanazawa, 2021).
Recently, Co-Zn-Mn compounds have emerged as a novel class of skyrmion-hosting chiral magnets (Tokunaga et al., 2015;Karube et al., 2016Karube et al., , 2018Karube et al., , 2020Henderson et al., 2021). This system crystallizes in the -Mn chiral cubic structure with either a P4 1 32 or P4 3 32 space group, and with 20 atoms distributed across the 8c and 12d Wyckoff sites [ Fig. 1(a)] (Hori et al., 2007;Xie et al., 2013;Bocarsly et al., 2019;Nakajima et al., 2019). For the composition line (Co 0.5 Zn 0.5 ) 20Àx Mn x (0 x 20), both density functional theory calculations (Bocarsly et al., 2019) and neutron diffraction show that magnetic Co preferentially occupies the 8c site, while magnetic Mn and non-magnetic Zn preferentially fill in on the 12d site (Bocarsly et al., 2019;Nakajima et al., 2019). For mixed composition samples, the simultaneous occupancy of both sites by just a single atomic species is never perfect, leading to inevitable compositional disorder. Nonetheless, the average -Mn structure is maintained for all x, thus describing compositions ranging from Co 10 Zn 10 to Mn 20 or -Mn itself Nakajima et al., 2019). Fig. 1(b) shows the low-temperature portion of a phase diagram that reports characteristic temperatures observed in magnetometry measurements versus Mn content x. The end member Co 10 Zn 10 (x = 0) is a high-temperature chiral magnet, where Co spins on the 8c site order helically with a period ' 150 nm below the transition temperature T c ' 420 K [beyond the upper temperature limit of Fig. 1(b)] and form an equilibrium skyrmion phase that is stable far beyond room temperature (Karube et al., 2020). In this low-x limit, the general paradigm of DMI chiral magnetism observed in structurally simpler chiral cubic magnets like the B20s broadly applies (Kanazawa et al., 2017).
Introduction of Mn leads to a rapid suppression of T c to far below room temperature [ Fig. 1(b)] and a decrease in the helical periodicity near T c -and hence in skyrmion size -from ' 130 nm in Co 9 Zn 9 Mn 2 to ' 110 nm in both Co 8 Zn 8 Mn 4 and Co 7 Zn 7 Mn 6 (Karube et al., 2020). As indicated by the shaded purple region in Fig. 1(b), for fixed compositions 2 < x < 6, below T c , decreases by $40-50% upon cooling between two temperatures T H < T < T L . This manifests as an increase in the magnitude of the helical propagation vector q (= 2/) measured by (a) The two -Mn-type crystal enantiomers of Co 6.75 Zn 6.75 Mn 6.5 viewed along the [111] direction. The 8c and 12d Wyckoff sites are coloured according to their average occupation of Co (blue), Zn (green) and Mn (red). (b) The low-temperature (T) versus Mn concentration x in (Co 0.5 Zn 0.5 ) 20Àx Mn x , for 0 x 8, determined from magnetization measurements. Circle and triangle symbols denote magnetic transitions identified previously from measurements on polycrystalline samples . Star symbols correspond to new data obtained from the Co 6.75 Zn 6.75 Mn 6.5 crystals studied here. The shaded purple region denotes a T range for which the magnetization at H = 20 Oe decreases, and concomitantly the helical wavevector q observed by SANS increases, for decreasing T. The square (diamond) symbols indicate temperatures where q starts increasing (stops increasing) on cooling, as denoted by T H (T L ). (c) The temperature dependence of the field-cooled (FC) and zero-field-cooled (ZFC) d.c. magnetization in single-crystal Co 6.75 Zn 6.75 Mn 6.5 . (d), (e) The temperature and frequency dependence of, respectively, the real ( 0 ) and imaginary ( 00 ) parts of the a.c. susceptibility of Co 6.75 Zn 6.75 Mn 6.5 in the low-T range. SANS, and indicates a reduction in the ratio of J/D. This behaviour is interpreted as arising due to an onset of antiferromagnetic-like correlations between Mn moments on cooling that affect the ferromagnetic interactions and DMI between Co (Karube et al., , 2020. At lower temperatures below T L , a reentrant spin glass transition T g is observed for 3 < x < 6, which is known to involve the 8c helical spin correlations (Karube et al., 2020). The origin of the spin-glasslike properties can be traced from the physics of the other end member, -Mn (x = 20), a well known elemental spin liquid (Nakamura et al., 1997). In its pure form, -Mn displays no spin glass transition, and the spin liquid property is due to the strong geometric frustration of antiferromagnetically coupled local Mn moments residing on the hyper-kagomé -coordinated 12d site. Spin-glass-like transitions emerge in lightly doped -Mn alloys, due to combined geometric frustration and compositional disorder (Nakamura et al., 1997;Stewart et al., 2002Stewart et al., , 2008Stewart et al., , 2010Stewart & Cywinski, 2009). In the presently studied composition line, no helical transition is seen for 6.5 < x < 19, and instead only a spin-glass-like transition T g is observed .
Overall, the phase diagram of the present class of Co-Zn-Mn chiral magnets combines various key ingredients in a single system, namely mainly Co DMI chiral magnetism on the 8c site, magnetic frustration mainly due to antiferromagnetic correlations between Mn spins on the 12d site, magnetic anisotropy that varies with T and x (Preißinger et al., 2021), and compositional disorder. Tuning the composition controls the relative influence of each aspect and has thus far led to a series of novel findings. These include the observation of equilibrium skyrmion phases near T c , both far above and far below room temperature (Tokunaga et al., 2015), and the facile disorder-assisted creation of supercooled metastable skyrmion states (Karube et al., 2016(Karube et al., , 2020Morikawa et al., 2017). These metastable skyrmion states are practically infinitely long lived, survive over the majority of the phase diagram, and display novel and reversible coordination transformations that preserve the topological charge carried by the skyrmions. Finally, in Co 7 Zn 7 Mn 6 the chiral magnetism and magnetic-frustration-induced fluctuations conspire to stabilize a second field-induced equilibrium skyrmion phase for temperatures just above T g Ukleev et al., 2021).
In this study we explore the helical, skyrmionic and short-range magnetic correlations in a new composition Co 6.75 Zn 6.75 Mn 6.5 with x = 6.5 by SANS, magnetometry, magnetic diffuse neutron scattering and Lorentz transmission electron microscopy (LTEM) measurements. As seen in Fig. 1(b), the transitions at T c and T g are closer together for this composition compared with 3 < x < 6, indicating that magnetic frustration and disorder compete more strongly with DMI chiral magnetism in this system. At the same time, in terms of a reduced temperature ÁT/ T c , the thermal extent of the equilibrium skyrmion phase has been found to grow progressively with x from 0.016 to 0.031 to 0.050 to 0.147 for x = 0, 2, 4 and 6, respectively (Karube et al., 2020), indicating an enhanced stability. Moreover, for x = 6, a second equilibrium skyrmion phase is observed far below T c , in accord with an enhanced stability of skyrmions. Therefore, it is important to understand how the helical magnetism and skyrmion phase stability evolve with x in the presence of competing interactions.
Here, we show experimentally that, for x = 6.5, the effects of magnetic frustration and disorder are so strong that they almost completely suppress the formation of the skyrmion phase near T c . Instead, SANS shows that the mesoscale spin correlations in the majority of the sample are dominated by strong magnetic disorder across the phase diagram. SANS nonetheless reveals that a $10% minority fraction of the sample does undergo a standard field-induced transition to a regime of skyrmion correlations near to T c with the thermal window of stability ÁT/T c ' 0.16. However, due to the generally strong magnetic disorder in the sample, the skyrmion correlations revealed by SANS are not clearly detectable by either magnetometry or LTEM. We discuss the results in the context of magnetic disorder induced on the 8c site through coupling with geometrically frustrated interactions on the 12d site. The important role of magnetic frustration is shown through direct measurement of short-range magnetic correlations in Co 6.75 Zn 6.75 Mn 6.5 by diffuse neutron scattering, from which characteristic couplings between Mn moments on 12d sites are estimated.

Sample preparation
Bulk single crystals of Co 6.75 Zn 6.75 Mn 6.5 were prepared by the Bridgman method. Single crystals were identified using X-ray Laue diffraction and their structural quality characterized at room temperature using Cu K radiation from a laboratory X-ray diffractometer (Rigaku, RINT-TTR III). Fig. 2 shows typical diffraction data obtained from the (110) structural peak of one crystal extracted from the growth. According to the 2 scan shown in Fig. 2(a) and the rocking scan shown in Fig. 2(b), the crystals display good structural quality with a finite mosaicity of less than 1 . Thus in the magnetic neutron scattering measurements that follow, the mosaic spread of the crystal can be considered unimportant with respect to the broad and diffuse magnetic scattering features observed. Further crystals were identified and cut from the same growth into regular-shaped platelets for both bulk magnetic and SANS measurements [ Fig. 3(a)]. The chemical composition was examined by an energy-dispersive X-ray (EDX) spectrometer (Bruker XFlash6) equipped with a scanning electron microscope (JEOL JSM-6701F). The composition determined by EDX is Co 6.73 (1) Zn 6.67 (2) Mn 6.60 (2) , close to the nominal composition.
Polycrystalline Co 6.75 Zn 6.75 Mn 6.5 for neutron diffuse scattering measurements was synthesized from pure Co, Zn and Mn metals with nominal concentrations. The metals were sealed in evacuated quartz tubes, heated at 1473 K for 12 h, cooled to 1173 K at 1 K min À1 , annealed for 24 h, and cooled down to room temperature (293 K) at 1 K min À1 . Phase purity with the -Mn-type structure was confirmed using X-ray diffraction.
For the LTEM measurement, a thin plate sample with a (001) surface and thickness $150 nm was prepared from a bulk single-crystal sample using a focused Ga ion beam.

Magnetometry measurements
Direct-current (d.c.) magnetization data for single-crystal Co 6.75 Zn 6.75 Mn 6.5 were acquired using the vibrating-sample magnetometer mode of a superconducting quantum interference device magnetometer (Quantum Design MPMS3). Alternating-current (a.c.) susceptibility measurements were carried out using the a.c. measurement mode of the MPMS3. Both the static magnetic field and the a.c. excitation field (1 Oe) were applied along a cubic axis. The a.c. frequency was chosen to be 193 Hz except for frequency-dependent measurements.

Neutron scattering measurements
SANS measurements on a 57.2 mg single-crystalline sample of Co 6.75 Zn 6.75 -Mn 6.5 were performed on the D33 beamline at the Institut Laue-Langevin (ILL), Grenoble, France . Neutrons with a wavelength of either 8 or 10 Å were collimated over a distance of 12.8 m before the sample. The scattered neutrons were detected by a two-dimensional position-sensitive multidetector positioned 12.8 m behind the sample. Data were collected over a range of momentum transfer 0.02 < q < 0.4 nm À1 [q = (4/ n )sin, where is half the scattering angle and n is the wavelength of the incident neutron beam].
For SANS the single-crystal sample was installed in a horizontal-field cryomagnet at the sample position on the beamline. As shown in Fig. 3(b), two experimental geometries were studied, namely H k k i and H ? k i , where k i is the incoming neutron wavevector which was chosen to be parallel to [100] for both geometries. In either geometry, the SANS measurements were done by collecting data as the cryomagnet and sample were rotated together around the vertical axis over the neutron beam access range of AE10 provided by the cryomagnet windows. Detector measurements obtained at a range of rotation angles were summed together to produce a single image showing the distribution of magnetic scattering. Unless otherwise stated, SANS data were obtained at each temperature and magnetic field after an initial zero-field cooling through the critical temperature $102 K, and a subsequent H ramp once at the target temperature. Further data obtained either in the paramagnetic regime at 120 K or in a field-polarized regime were used for background subtraction of the low-T /low-H data to leave just the magnetic SANS signal of interest. SANS data reduction and analysis were performed using the GRASP software developed at the ILL (Dewhurst, 2003).
Magnetic diffuse neutron scattering (MDNS) experiments on a 17.9 g polycrystalline sample of Co 6.75 Zn 6.75 Mn 6.5 were carried out on the D7 beamline at the ILL ). An xyz polarization analysis allowed pure isolation of the magnetic scattering cross section from the total scattering . The sample was loaded into a doublewalled Al container and installed in a standard Orange He cryostat. For the experiment, an incoming neutron wavelength of 3.1 Å was used, and data were collected over a range of momentum transfer 0.6 < q < 3.8 Å À1 (or equivalently 6 < q < 38 nm À1 ).

LTEM measurements
LTEM measurements were performed with a transmission electron microscope (JEOL JEM-2800). A magnetic field was applied perpendicular to the plate, i.e. parallel to [001], and its  (a) A photograph and the crystal orientation of the Co 6.75 Zn 6.75 Mn 6.5 single crystal studied by SANS. (b) Schematic diagrams of the two experimental geometries studied by SANS. In each geometry the neutron beam direction (k i ) is normal to the largest face of the plate-like sample. The geometries differ according to the direction of the magnetic field H, with H k k i on the left and H ? k i on the right. (c)-(g) SANS patterns measured during ZFC at 100, 90, 80, 50 and 1.5 K, respectively. The intensity scale of the colour plot varies in each panel. The crystal orientation indicated for the SANS patterns in panels (c)-(g) is the same as for panel (a). magnitude was controlled by tuning the objective lens current of the microscope.

Demagnetization calibration
For single-crystal measurements, the relative demagnetization factors between measurement configurations with H parallel to the sample plate (d.c. and a.c. susceptibility, and SANS in the H ? k i geometry) and H perpendicular to the sample plate (SANS in the H k k i geometry) are different. To cater for the difference in demagnetization, data presented throughout this article with H parallel to the sample plate have had the field scale calibrated higher so that

Results and discussion
3.1. Magnetometry measurements Fig. 1(c) shows the temperature (T)-dependent magnetization (M) in single-crystal Co 6.75 Zn 6.75 Mn 6.5 . The data are obtained in a small magnetic field of 20 Oe, either on field cooling (FC) or on field warming after an initial zero-field cooling (ZFC). In the high-T region for both curves, M(T) clearly increases (decreases) on the FC (ZFC) process. A transition temperature at T c ' 102 K between helical and paramagnetic regimes is estimated from the inflection point of M ZFC (T), though it is noted that the transition is smeared over a broad T range compared with lower-x compounds (Karube et al., 2020). Below 80 K, M FC (T) falls with decreasing T, and a clear separation between the M FC (T) and M ZFC (T) curves at $65 K can be interpreted as the onset of spin-glass-like behaviour.
To investigate the low-T behaviour further, Figs. 1(d) and 1(e) show the temperature and frequency dependence of, respectively, the real ( 0 ) and imaginary ( 00 ) parts of the a.c. susceptibility. A frequency dependence of 0 and 00 is a common spin glass characteristic, though in the present sample it is modest and exists over a broad thermal range. At the same time, no thermally sharp spin glass transition is seen. Therefore, while the material displays some tendency towards glassy behaviour at low temperature, further investigations are needed to determine if the low-temperature regime can be properly allocated as a spin glass. Here, for consistency with previous work on lower-x compounds (Karube et al., 2020), in Figs. 1(b) and 1(c) we use the label T g to denote the temperature where M ZFC (T) shows an inflection point, and thus the temperature where spin-glass-like behaviour is most clearly inferred in the data. For the present compound T g ' 53 K can be compared with $65 K, which is where the magnetization hysteresis vanishes.
Overall, the bulk magnetic measurements are hallmarked by transition features -labelled T c and T g -that are thermally smeared. This contrasts strongly with sharper transitions observed at lower x, including the nearby composition Co 7 Zn 7 Mn 6 (x = 6), indicating comparatively stronger disorder of the magnetically correlated phases in the present x = 6.5 composition which is likely to be manifested in the low-T magnetic spin configurations.

SANS measurements of helical and skyrmion correlations
3.2.1. Helical disordering during zero-field cooling. To shed more light on the magnetometry data, we next turn to SANS investigations of the mesoscale magnetic spin correlations in a Co 6.75 Zn 6.75 Mn 6.5 single crystal. Figs. 3(c)-3(g) show SANS patterns collected at selected temperatures during ZFC. Just below T c at 100 K, the pattern shown in Fig. 3(c) is composed of two peaks with propagation vectors aligned with the [010] direction co-existing with an isotropic ring of scattering intensity. The intensity ring is indicative of incommensurate helical spin correlations with full orientational disorder, while the peaks are more typical for an incommensurate helical order with finite orientational order. The alignment of a helical propagation vector with the cubic axis is consistent with that observed in other Co-Zn-Mn compounds with finite Mn content (Karube et al., 2016(Karube et al., , 2020, perhaps indicating that the sign of magnetic anisotropy in x = 6.5 is the same as that observed for 2 x 6 ( Karube et al., 2020;Preißinger et al., 2021). According to the cubic symmetry, additional peaks would be expected in this scattering plane due to a helical domain with propagation vectors aligned with the [001] direction. The observation of only two peaks indicates a preferential helical domain selection effect, which may be due to a residual sample strain.
On cooling to lower T, the two peaks seen at 100 K quickly broaden azimuthally, so that by 80 K the full decay of the orientational order of all helical spin correlations in the sample is complete and the entire SANS intensity appears as a ring around the origin of reciprocal space. On cooling further to the base temperature of 1.5 K, the intensity of the ring becomes weaker compared with higher T and is distributed over an extended range in |q|, thus reflecting a reduction in the radial correlation length. At all temperatures, the correlation length normal to the detector plane determined by sample rotation-angle-dependent (i.e. rocking curve) measurements remains nearly angle independent (data not shown). Overall, the ZFC data show that the sample always displays mainly three-dimensionally disordered helical spin correlations, with a clear reduction in the radial correlation length taking place on cooling.
With Fig. 4, we analyse more quantitatively the magnetic SANS intensity observed during ZFC. Fig. 4(a) shows the radial |q| dependence of the SANS intensity integrated over all azimuthal angles. At all temperatures, the profiles are fitted well by a Lorentzian function, indicating the exponential decay of the radial correlation function with distance. The fitted function at each T is I(q) = I 0 + (2A/){w/[4(q À q 0 ) 2 + w 2 ]}, where I 0 is a fitted constant background, A is the fitted integrated intensity of the peak, w is the fitted peak FWHM and q 0 is the fitted peak centre. The temperature dependence of parameters A, w and q 0 is shown in Figs. 4(b)-4(d).
From Fig. 4(b) we observe the integrated intensity A to rise initially on cooling below T c , before decreasing over the range from $80 to $40 K and then remaining approximately constant down to 1.5 K. The reduction in A over the intermediate temperature range largely coincides with significant enhancements of both q 0 [ Fig. 4(c)] and w [ Fig. 4(d)]. Finally, all fitted quantities stop evolving with temperature after cooling below $40 K, consistent with being in a spin-glass-like regime.
The observed increase in q 0 on cooling implies a reduction in the helical periodicity = 2/q 0 , from 89 (1) nm near to T c to 62 (1) nm by the base temperature. Qualitatively similar temperature dependences in A and q 0 , as observed in Fig. 4, are also seen in the 2 x 6 compounds (Karube et al., 2016(Karube et al., , 2020 and are understood to indicate the development of antiferromagnetic-like correlations on cooling. These antiferromagnetic correlations are known to serve as magnetic defects, as shown by the dramatic increase in spin wave damping observed in Co 8 Zn 8 Mn 4 (Ukleev et al., 2022). The increase in w over the same T range shows the gradual development of magnetic disorder in terms of the reduction of the radial correlation length, which itself provides a measure of the size of helical domains along the average direction of q 0 . This reduction in the radial correlation length could contribute to the apparent reduction in A between $80 and $40 K implied by our analysis, but we stress that a full treatment of the temperature dependence of A requires complete measurement of the scattering intensity distribution both within and normal to the detector plane. As mentioned above, it was not possible to measure the latter due the inherently short longitudinal magnetic correlation lengths, which cause the intensity distribution normal to the detector plane to extend far beyond the experimentally accessible range allowed by the cryomagnet windows. Therefore, further investigations designed to measure the full scattering intensity are needed for the accurate determination of the temperature dependence of A.
Turning to the fitted values of w shown in Fig. 4(d), they are seen to be always significantly larger than the instrumental resolution, allowing a simple estimation of the radial correlation length using ' 1/w. We find that the radial correlation length near to T c is $25 nm, i.e. of the order of 40 cubic unitcell spacings, before it falls on cooling to $7 nm below T g , which is just above 10 cubic unit-cell spacings. It is notable that is always shorter than , which indicates that the helical spin correlations are typically only short-range ordered. Such a tendency towards helical short-range order can reflect competing magnetic interactions on the mesoscale in this system, while we also note that, according to theory, defectinduced disorder can contribute further to the broadening of the helical Bragg peak (Utesov et al., 2015).
The general behaviour observed in the ZFC temperature dependence of the A, w and q 0 parameters in Co 6.75 Zn 6.75 Mn 6.5 (x = 6.5) bears qualitative similarity to that observed in the 2 x 6 compounds (Karube et al., 2016(Karube et al., , 2020. In comparison with the lower-x compositions however, the magnetic disorder and disordering process on ZFC in the present x = 6.5 sample is clearly more pronounced. Firstly, by 80 K, the minority sample fraction of helical-like order showing up as SANS peaks at 100 K undergoes a full loss of orientational order by 80 K. The full loss of helical orientational order is not observed in any sample from 0 x 6 on ZFC down to base temperature. Secondly, this is followed by the strongest reduction in the radial correlation length amongst the studied compositions (Karube et al., 2016(Karube et al., , 2020. The present results thus extend to x = 6.5 the empirically observed inverse correlation between the increase in Mn concentration x and the stability of helical order at low T for 0 x 6. In addition, the present data imply that the x = 6.5 sample provides a future opportunity for detailed studies of an unusual melting of the helical correlations on cooling from T c to T g , and potentially spiral spin liquid characteristics (Gao et al., 2017).

Skyrmion correlations in a finite magnetic field.
Next, we turn to measurements in a finite magnetic field. Figs. 5(a) and 5(b) show SANS patterns obtained in the H k k i geometry at 90 K, and in zero field and at 18 mT, respectively. The pattern in zero field is consistent with that shown in Fig. 3(d), where the SANS intensity forms a ring-like structure with more intensity on the right-and left-hand sides due to azimuthally broadened helical spots. Application of the magnetic field leads to a homogenization of the intensity distribution such that it forms a near isotropic intensity ring by 18 mT [Fig. 5(b)]. As will be supported from measurements in the H ? k i geometry, this H-driven rearrangement of the intensity is consistent with a field-induced transition of helical spin correlations into orientationally disordered skyrmion lattice correlations, as opposed to an H-driven disordering process.   observed. In zero field, the intensity in the red sector box pair is only 12 (2)% larger than that in the blue sector box pair, showing that the majority of the observed SANS intensity is due to the ring-like intensity component. The difference between the red and blue curves falls monotonically as the field is increased, eventually forming a fully azimuthally isotropic intensity distribution that survives until saturation.
Figs. 5(d)-5(e) show the SANS data obtained at 90 K in the H ? k i geometry, in zero field and at 18 mT. In this geometry, the pattern obtained at 18 mT shows the magnetic field to drive the partial rearrangement of the ring-like intensity in zero field so that there are two clear intensity maxima aligned with the vertical [001] direction. Since, in chiral cubic magnets, the skyrmion lattice forms with propagation vectors distributed in the plane perpendicular to the magnetic field, the emergence of additional top/bottom SANS intensity seen clearly in Fig. 5(e) corresponds to a hallmark signature for two-dimensional skyrmion lattice correlations (Mü hlbauer et al., 2009;Karube et al., 2016). In Fig. 5( f ) the formation of the skyrmion tubes aligned with H is manifested as a magnetic field range for which the combined intensity in the two top/ bottom (blue) 90 sectors is maximally $20% larger than those of the two left/right (green) 90 sectors. On further increase in the field, the relative intensity of the green sector box pair becomes larger than that of the blue sector box pair before saturation. This can be understood in terms of the generally enhanced susceptibility of helical (or conical) spin correlations when the field is applied in the direction of propagation. Therefore, the SANS intensity due to helical spin correlations propagating relatively close to the applied field direction survives to higher fields compared with helical and skyrmion correlations propagating along directions far away from the direction of H.
By 70 K, no magnetic-field-driven rearrangement of the SANS intensity is observed that is consistent with a conventional skyrmion formation signature in chiral magnets. Fig. 6 shows the relevant SANS data and data analysis at this temperature, which are analogous to those shown in Fig. 5 obtained at 90 K. In the H k k i geometry, Figs. 6(a) and 6(b), respectively, show the SANS patterns obtained in zero field and at 28 mT. In each case, the azimuthal distribution of the SANS intensity appears isotropic around the origin, with this confirmed at all fields in the H scans by the quantitative analysis presented in Fig. 6(c). For the H ? k i geometry, Figs. 6(d) and 6(e) show that the intensity ring in zero field evolves with increasing H so that there is slightly more intensity on the left-and right-hand sides at 30 mT. This is borne out by the quantitative analysis shown in Fig. 6( f), which shows that as H increases the SANS intensities extracted from the green left/right sector boxes [inset Fig. 6( f )] remain higher until saturation. Similar to the behaviour at 90 K, this can be understood in terms of the higher susceptibility for helical correlations propagating closer to the direction of H. Importantly, the analysis shows that, by 70 K, no standard signature of equilibrium skyrmion formation is detected, and the magnetic state is always predominantly    three-dimensionally disordered. Further measurements confirm that this picture prevails down to the base temperature.
To summarize the H-dependent measurements on singlecrystal Co 6.75 Zn 6.75 Mn 6.5 , in Fig. 7 we present phase diagrams constructed from the real part of the a.c. magnetic susceptibility 0 [Figs. 7(a) and 7(b)] and SANS [Figs. 7(c) and 7(d)] data. Figs. 7(a) and 7(b) show phase diagrams constructed from, respectively, H-increasing and H-decreasing scans done at constant temperature. These two phase diagrams are very similar, and bear little resemblance to those of either low-x (Co 0.5 Zn 0.5 ) 20Àx Mn x compounds (Karube et al., 2020) or archetypal chiral magnets such as MnSi (Mü hlbauer et al., 2009) and Cu 2 OSeO 3 (Seki et al., 2012). In the lattermentioned systems, 0 measurements are particularly useful for identifying the extent in T and H of different phases (Bauer & Pfleiderer, 2012;Birch et al., 2020). In the present case, the most striking features are the T-smeared low-field transitions at T c and T g , the vanishing of 0 for T < T g ' 50 K, and the monotonic H variation of 0 in the region of T g < T < T c (H). In contrast to clear signatures in 0 revealing magnetic phase transition boundaries in chiral magnets like the B20s, no fine structure in 0 is identifiable from the present sample, and none indicating skyrmion formation. Instead, 0 is presumably dominated by the temperature evolution of the majority fraction of disordered helical spin correlations, and the spinglass-like properties at low T.
In contrast, the signature for skyrmion formation shows up more clearly in phase diagrams constructed from SANS data obtained in the H ? k i geometry, for both H-increasing [ Fig. 7(c)] and H-decreasing [ Fig. 7(d)] scans at constant temperature. The colour scale describes the ratio of summed SANS intensities measured in the blue top/bottom sector boxes [denoted I(' = 0 )] to that determined from the green left/right sector boxes [denoted I(' = 90 )]. In both phase diagrams, and in the field-reversible region T g < T < T c (H), the red portion of the colour plots indicates the excess of intensity in the top/bottom sectors, providing the clearest indication for the thermodynamic conditions under which skyrmions may form in the system. The location of this red portion of the phase diagram is similar to that for the conventional twodimensional skyrmion A phase in chiral cubic magnets, namely occupying a narrow temperature region directly below T c and at finite H. In quantitative terms, the thermal extent of the A phase in reduced temperature T/ T c is $0.16, which is comparable to that in Co 7 Zn 7 Mn 6 , but the intensity ratio between the blue and green pairs of integration sectors in the 'skyrmion phase' is only $1.2 and the majority of the SANS intensity nonetheless remains attributable to the disordered helical correlations. From this perspective, the skyrmion phase is largely suppressed in the present Co 6.75 Zn 6.75 Mn 6.5 sample compared with lower x compositions. Apart from the minority skyrmion phase, disordered helical configurations dominate the phase diagram above T g and for fields below saturation, with the green colours indicating ratios between blue and green sector box intensities that are closer to 1. Finally, in the region below T g , there is a pronounced irreversibility in the intensity ratio defined by the colour scale between the H-increasing and H-decreasing phase diagrams, consistent with that expected from a spin-glass-like regime.

Lorentz transmission electron microscopy
As it is one of the key experimental tools for studying helical and skyrmion spin textures in chiral magnets (Kanazawa et al., 2017;Huang et al., 2018;Tokura & Kanazawa, 2021), we employed LTEM with the aim of direct visualization of the magnetic textures below T c in a thin plate sample of Co 6.75 Zn 6.75 Mn 6.5 . Fig. 8(a) shows the phase diagram of Fig. 7(c), with labels indicating the T and H conditions under which the LTEM images shown in Figs. 8(b)-8(d) were obtained. In all images, neither periodic magnetic textures nor (isolated) topological skyrmions can be identified. This indicates the magnetic contrast to be extremely weak, which is presumably due to the strong magnetic disorder, not only within the plane but also along the sample thickness. This contrasts with LTEM studies on lower-x compounds, including x = 6, where unambiguous imaging of helical order and skyrmions has been performed despite the existence of moderate magnetic disorder (   Since estimates for H c were difficult to obtain from the a.c. susceptibility data (due to its very smooth H dependence), the same values for H c determined from the SANS data are plotted on colour maps shown in panels (a) and (b).

Magnetic diffuse neutron scattering
Finally, we turn to magnetic diffuse neutron scattering measurements from a Co 6.75 Zn 6.75 Mn 6.5 powder sample taken using the D7 spectrometer at the ILL. With these measurements we explore magnetic neutron scattering at higher momentum transfers than afforded by SANS, which extend down to atomic length scales. In particular, we seek experimental evidence for persistent short-range magnetic correlations. Earlier work on -Mn-type samples shows structured magnetic diffuse scattering to be a common experimental signature for short-range correlations of Mn moments on the 12d site (Stewart et al., 2008(Stewart et al., , 2010Stewart & Cywinski, 2009;Paddison et al., 2013). The origin of the scattering is ascribed to the strong geometric frustration of interacting Mn moments on the 12d site with its frustration-inducing hyperkagomé geometry. It is notable that qualitatively similar magnetic diffuse scattering was reported from measurements on the Co 7 Zn 7 Mn 6 (x = 6) compound . Since the average 12d occupation for x = 6 is Co : Zn : Mn = 0.2 : 7.0 : 4.8 (Nakajima et al., 2019), it becomes clear that only partial average occupation of the 12d site by magnetic Mn ions is needed for magnetic diffuse scattering to show up. In this context it can be expected that a similar experimental signature is observed for the present x = 6.5 composition, since the average Mn content of the 12d site is only slightly higher, namely Co : Zn : Mn = 0.25 : 6.75 : 5.0 (Nakajima et al., 2019).
Using the xyz polarization analysis method on D7, the nuclear coherent, magnetic and nuclear spin-incoherent scattering cross sections are straightforwardly and cleanly isolated from the total scattering observed ). Fig. 9(a) shows these various scattering cross sections measured from Co 6.75 Zn 6.75 Mn 6.5 powder as a function of modulus wavevector |q| at 2 K and zero magnetic field. The nuclear spin-incoherent scattering intensity displays no |q| dependence as expected, while in the nuclear coherent scattering both structural diffraction peaks and diffuse scattering due to structural disorder are observed. Since the studied q range is too limited to extract detailed information on the origin of the structural diffuse scattering, in what follows we focus on the magnetic diffuse scattering. Fig. 9(b) shows a closer view of the observed magnetic diffuse scattering cross section versus |q|. The scattering is composed largely of a peak that is broad in momentum   (a) Neutron diffuse scattering measurements as a function of modulus wavevector |q| from a Co 6.75 Zn 6.75 Mn 6.5 powder sample at 2 K. The total observed scattering cross section is shown by black symbols. Using xyz polarization analysis, the nuclear coherent (blue symbols), nuclear spinincoherent (green symbols) and magnetic (red symbols) scattering cross sections are extracted from the total scattering. Grey dashed lines indicate nuclear peak positions due to Al Bragg scattering from both the cryostat and sample container. (b) A closer look at the pure magnetic component of the total scattering cross section. Both grey and red symbols represent the entire measured profile. Grey symbols denote either clear or suspected Bragg scattering, and are excluded from the data set for the purposes of fitting the mean-field model to the data. Two fits of the mean-field model discussed in the text are shown. The blue solid line corresponds to a fit of a mean-field model that takes into account just a single nearest-neighbour antiferromagnetic interaction on the 12d site, J 1 = À0.53 meV. The black dashed line shows the improved fit of the mean-field model when taking into account a second nearest-neighbour interaction J 2 . In this case the fitted parameters are J 1 = À0.67 meVand J 2 = 0.67 meV, indicating a probable combination of both antiferromagnetic and ferromagnetic interactions on the 12d site. transfer around |q| ' 1.7 Å À1 , with additional weak peak-like features that are consistent with being due to the disordered helical correlations observed by SANS. For further data treatment and analysis of the magnetic diffuse scattering, we follow the same approach reported for x = 6 . Namely, the weak peaks are removed and the remaining diffuse scattering is fitted to a mean-field model that accounts for the paramagnetic scattering due to interactions between Mn-Mn moments occupying the 12d site. Further technical details for the calculation method are reported by Ukleev et al. (2021). Here we mention that, for simplicity, similarly to the approach of Ukleev et al. (2021), an average crystal structure model is assumed, as well as a 12d site that is fully occupied by magnetic moments. The blue line in Fig. 9(b) shows the fit according to this minimal model that considers just a single nearest-neighbour antiferromagnetic exchange constant with fitted J 1 = À0.53 meV, and a non-interacting temperaturedependent spin susceptibility. The reasonable fit of the model makes it plausible that the diffuse scattering is due to frustrated nearest-neighbour antiferromagnetic Mn-Mn interactions on the 12d site. The fitted value of J 1 is essentially identical to that found for x = 6 (J 1 = À0.54 meV), consistent with the observation that the diffuse scattering profiles from the two compounds are quantitatively similar. Inclusion in the model of a second nearest-neighbour ferromagnetic interaction J 2 leads to an improvement in the fit, as shown by the black dashed line in Fig. 9(b). The fit yields J 1 = À0.67 meV and J 2 = 0.67 meV, which have the same magnitude but opposite sign, thus implying that the proper description for the distribution of magnetic diffuse scattering involves a combination of competing antiferromagnetic (J 1 ) and ferromagnetic (J 2 ) interactions. While future studies on single-crystal samples are needed to quantify the interactions more rigorously, at the level of the data and analysis shown here, it is reasonable to conclude that the origin of magnetic diffuse scattering involves a major contribution from nearestneighbour antiferromagnetic interactions between Mn moments on the 12d site.

Discussion
Our neutron scattering and magnetometry measurements reveal that the interactions and compositional disorder in the chiral magnet Co 6.75 Zn 6.75 Mn 6.5 conspire to generate magnetically disordered phases at low temperature, over both atomic and mesoscopic length scales. As deduced in previous studies of Co-Zn-Mn compounds, mesoscale helices and skyrmions originate from the chiral magnetism of spins occupying the 8c site, involving mainly ferromagnetic Co ions (Karube et al., 2016(Karube et al., , 2020Bocarsly et al., 2019;Ukleev et al., 2019Ukleev et al., , 2021. For 0 < x < 3, antiferromagnetic Mn fills in exclusively onto the geometrically frustrated 12d site, while for x > 3 Mn starts to fill in and replace Co on the 8c site too (Nakajima et al., 2019). As borne out by the sharp suppression of T c , the emergence of spin glass behaviour and the tendencies towards magnetic disorder, adding Mn is generally unfavourable for mesoscale chiral magnetism. At the same time, however, the reduced temperature (T/ T c ) extent of the high-temperature skyrmion phase progressively increases with x for the 3 < x < 6 compounds, implying that Mn substitution effectively enhances skyrmion phase stability within the phase diagram (Karube et al., 2020). In the following, we discuss the origin of the disordered mesoscale magnetism and the suppression of the equilibrium high-temperature skyrmion phase in the x = 6.5 sample.
As seen in Fig. 1(b), compared with lower-x compounds, an important aspect of the present x = 6.5 system is that the characteristic temperatures T c and T g are closer together, which already indicates a closer competition between chiral magnetism on the one hand, and atomic-scale frustration and disorder on the other. In addition, the location of T c itself is also important in relation to the characteristic temperatures T H and T L , which bound the temperature range over which the helical q and degree of mesoscale disorder both increase on cooling for 3 < x < 6. Both of these effects are understood to reflect the developing role of correlations involving Mn moments on both the 8c and 12d sites (Karube et al., 2020). For x = 6.5, T c already lies between the values of T H and T L that would be expected for this composition according to an extrapolation of their lower x dependences. In turn, this implies that, when helical correlations begin to form, Mn spin correlations detrimental to long-range order are already present, and thus mesoscale magnetism that is largely only short-range ordered is observed, together with the nearcomplete suppression of the high-temperature skyrmion phase.
Overall, the data across all low-x compositions indicate that when the Mn spin correlation onset temperature T H < T c , i.e. for 3 < x 6 where helical long-range order occurs on cooling below T c , progressive introduction of Mn enhances hightemperature skyrmion phase stability in terms of T /T c , despite a concomitant increase in mesoscale disorder. This tendency ends when T c < T H , and pre-existing inter-site Mn spin correlations dominate the helical ordering process such that skyrmions can no longer form. We also stress that the suppression of the skyrmion phase for x = 6.5 could not be expected by merely examining the x dependence of T c and T g alone, with SANS measurements proving crucial to obtain the necessary microscopic picture.
Next we discuss the mesoscale magnetic disorder in Co 6.75 Zn 6.75 Mn 6.5 (x = 6.5). As mentioned above, our SANS data show the mesoscale magnetism to be dominated always by a majority fraction of fully orientationally disordered helical spin correlations. On ZFC below T c , further magnetic disordering via the reduction of the radial correlation length takes place, which is quantitatively stronger than that observed in lower-x compounds, including the nearby composition Co 7 Zn 7 Mn 6 (x = 6) . While a detailed description of the ZFC helical disordering process presents an interesting challenge for theory, we point out that a key ingredient must lie with the degree of Co-Mn mixing on the 8c site. According to neutron diffraction, the average 8c occupation for Co 6.75 Zn 6.75 Mn 6.5 is Co : Zn : Mn = 6.5 : 0 : 1.5, while for Co 7 Zn 7 Mn 6 it is Co : Zn : Mn = 6.8 : 0 : 1.2 (Nakajima et research papers 1228 Jonathan S. White et al. SANS study of magnetism in Co 6.75 Zn 6.75 Mn 6.5 al., 2019). In general, for the 8c site containing a majority Co/ minority Mn mixture, the ferromagnetic Co exchange field can be expected to drive a ferromagnetic alignment of small ordered Mn moments just below T c , so that these Mn moments do indeed contribute to helically modulating spin correlations. This picture has been confirmed in both Co 8 Zn 8 Mn 4  and Co 7 Zn 7 Mn 6  by element-selective resonant X-ray scattering measurements. On cooling below T H , the development of couplings between growing 8c Mn moments and erstwhile magnetically disordered 12d Mn moments competes with the Co exchange field. This will result in disordering due to the random deviation of 8c Mn moments on cooling, as they tend towards a disordered ground state native to very Mn-rich compounds. In this qualitative picture, the tendency towards increasingly disordered helical textures will clearly be stronger in Mn-richer Co 6.75 Zn 6.75 Mn 6.5 compared with lower-x compounds, consistent with SANS observations (Karube et al., 2016. Further contributions to the mesoscale disorder are also expected to arise due to the compositional disorder which will modify locally the atomic scale interactions such as the DMI. Theory shows that such a bond disorder can distort helical spirals and contribute to the broadening of the SANS peaks (Utesov et al., 2015).
Concerning topological skyrmions, our SANS measurements provide convincing evidence for the formation of conventional quasi-two-dimensional, yet in-plane orientationally disordered, static skyrmion correlations in a minority fraction of the Co 6.75 Zn 6.75 Mn 6.5 sample. These correlations are stable in a portion of the phase diagram that is similar to the conventional skyrmion phase just below T c in chiral magnets, and their presence is not obviously identifiable from the magnetometry and LTEM data at hand. An explanation as to why skyrmions exist only as a minority phase in Co 6.75 Zn 6.75 Mn 6.5 is difficult to ascertain unambiguously, but it may lie with randomly distributed local anisotropies induced by correlated structural disorder. Such local anisotropies could cause a local fine tuning of interactions so that pinning and disorder effects are less important, and a fraction of zerofield helical correlations are able to transform into skyrmions near to T c .
Clearly in Co 6.75 Zn 6.75 Mn 6.5 we obtain no experimental evidence for a low-temperature skyrmion phase far from T c , which contrasts with the observation of a second, lowtemperature, equilibrium skyrmion phase in Co 7 Zn 7 Mn 6 . Since no low-temperature skyrmion phase is found in the lower-x neighbouring composition Co 8 Zn 8 Mn 4 (Karube et al., 2016(Karube et al., , 2020 either, this makes Co 7 Zn 7 Mn 6 special amongst the Co-Zn-Mn compounds. From comparative muon spin relaxation studies of Co 8 Zn 8 Mn 4 and Co 7 Zn 7 Mn 6 , it was argued that a key ingredient for low-temperature skyrmion phase stability in Co 7 Zn 7 Mn 6 is the low-temperature frustration-induced fluctuations of the 12d Mn moments . According to the muon data, the associated density of magnetic fluctuations in the muon time window (typically the megahertz range) becomes particularly more pronounced at low temperature in Co 7 Zn 7 Mn 6 compared with Co 8 Zn 8 Mn 4 . Although no equivalent muon data exist for Co 6.75 Zn 6.75 Mn 6.5 , it can be expected that megahertz fluctuations are also significant at low temperature in this system due to the higher Mn content. Thus, while the density of frustration-induced magnetic fluctuations is simply too low to assist with lowtemperature skyrmion phase stabilization in Co 8 Zn 8 Mn 4 , in Co 6.75 Zn 6.75 Mn 6.5 their density is likely to be at least comparable to that of Co 7 Zn 7 Mn 6 , but insufficient to stabilize skyrmions out of the strongly disordered low-temperature helical background. In general, muon spin relaxation experiments detect pronounced megahertz magnetic dynamics in and around the skyrmion phases of a number of chiral magnets (Hicken, Holt et al., 2021;Ukleev et al., 2021). This makes the development of theoretical models for their origin at low temperature important, in order to test suggestions that they provide a route towards skyrmion phase stability.
Finally, we comment on the future perspectives for neutron scattering from quantum materials such as Co 6.75 Zn 6.75 Mn 6.5 . In the present system, we observe both structural and magnetic correlations with short-and long-range ordered character, over a broad range of momentum transfer that includes the conventional SANS range. It is clear that in complex quantum materials such as the Co-Zn-Mn intermetallics the eventual development of accurate theoretical models requires comprehensive measurement of structural and magnetic correlations over multiple length scales. While in principle the relevant scattering data can be pieced together from measurements done on different instruments covering the different dynamic ranges, for reasons of absolute scaling of scattering intensities and the avoidance of systematic uncertainties it is desirable to develop instrumentation capable of providing insight on the equal time correlations over a continuous extended range of momentum transfer. The data obtained from such instruments will facilitate the construction of atomistic theoretical models for multiple-length-scale magnets (such as Co-Zn-Mn compounds), which are needed for describing simultaneously the existence of magnetic longand short-range order on both mesoscopic and atomic scales.

Conclusions
Using small-angle neutron scattering, magnetometry, Lorentz transmission electron microscopy and magnetic diffuse neutron scattering, we have investigated the microscopic helical and skyrmion correlations in the chiral magnet Co 6.75 Zn 6.75 Mn 6.5 (T c ' 102 K). SANS experiments reveal that, below T c , the mesoscopic phase diagram is dominated by orientationally disordered helical correlations that are largely unresponsive to applied magnetic fields below the saturation field. Close to T c , a minority fraction of helical correlations in the sample undergo a magnetic-field-driven transformation into conventional two-dimensional skyrmion correlations. The signature for skyrmion formation is not obviously observed in magnetometry or LTEM measurements, highlighting the power of SANS to reveal the existence of skyrmions in this particular case, due its ability to probe the entire sample volume.
The characteristically strong magnetic disorder observed on both mesoscopic and atomic length scales is argued to arise from the interplay between compositional disorder, in particular the random mixing of magnetically distinct Co and Mn moments on the 8c Wyckoff site, and the magnetic frustration of Mn moments occupying the 12d Wyckoff site. While shortrange magnetic correlations due to 12d frustrated Mn-Mn interactions lead to the observed magnetic diffuse scattering on atomic length scales, the mesoscale order observed by SANS is due to modulating moments on the 8c site. To explain the unusual temperature-dependent disordering process of helically modulating 8c moments, we invoke a temperaturedependent coupling between Mn moments on the 12d and 8c sites that grows on cooling and promotes increasing mesoscale magnetic disorder due to random reorientations of erstwhile helically modulating 8c Mn moments. It is also likely that this strong tendency towards magnetic disorder on cooling prevents the stability of a second, low-temperature, skyrmion phase in Co 6.75 Zn 6.75 Mn 6.5 , which is different from what is observed in the nearby composition Co 7 Zn 7 Mn 6 .
Our study of Co 6.75 Zn 6.75 Mn 6.5 also highlights a general need for neutron instrumentation that can provide continuous access to an extended range of momentum transfer that includes the SANS range, so that the magnetic correlations in multiple-length-scale magnets like the Co-Zn-Mn family can be measured comprehensively, thus facilitating the development of appropriate theoretical models.